Efficient dispersion correction for FMCW radar in a tube

Abstract

Method for determining a distance to a surface of a medium (101, 108) or to another radar target in a tube (102, 107) using a radar measuring device (104, 111) which operates according to the principle of FMCW radar, wherein the method comprises: a) Emitting a frequency-modulated radar transmission signal (213) according to the FMCW principle inside the tube (102, 107), b) Receiving a radar reception signal reflected back from the surface of the medium (101, 108) or from the other radar target in the tube (102, 107) to the radar measuring device (104, 111), c) Mixing the radar received signal with the radar transmitted signal (213) or a signal derived therefrom and generating an intermediate frequency signal (211), d) Determining (505) a frequency spectrum of the intermediate frequency signal or a signal derived therefrom by means of a fast Fourier transform and detecting (506) the position of the frequency peaks in the frequency spectrum, e) Determining (508) a dispersion correction to eliminate or reduce dispersion effects, applying the dispersion correction to the intermediate frequency signal or a signal derived therefrom and producing a dispersion-corrected signal, f) Re-determining (510) the position of the frequency peaks in the frequency spectrum of the dispersion-corrected signal by f1) Introducing a number of frequency support points (603) in the area of ​​the frequency peaks detected in step d), f2) Determining the respective frequency amplitude selectively at the newly introduced frequency support points (603) using discrete Fourier transform or using the Goertzel algorithm, f3) Determining the position (604) of the frequency peaks in the frequency spectrum of the dispersion-corrected signal using the frequency amplitudes at the newly introduced frequency support points (603) and deriving the distance (513) to the surface of the medium or to the other radar target in the tube from the position (604) of the frequency peaks in the frequency spectrum.

Description

[0001] The invention relates to a method for determining a distance to a surface of a medium or to another radar target in a pipe by means of a radar measuring device according to claim 1. Furthermore, the invention relates to a radar measuring device for determining a distance to a surface of a medium or to another radar target in a pipe according to the preamble of claim 16.

[0002] In process automation technology, field devices are often used to record and / or influence process variables. Examples of such field devices include level measuring devices, mass flow meters, pressure and temperature measuring devices, etc., which act as sensors to record the corresponding process variables: level, flow, pressure, or temperature.

[0003] In principle, field devices are all devices that are used close to the process and that provide or process-relevant information.

[0004] A large number of such field devices are manufactured and distributed by Endress+Hauser.

[0005] Using radar measuring devices based on FMCW radar, the fill level in a container or tank can be measured precisely. However, radar measurements in a pipe produce special effects because the pipe acts as a waveguide for the radar waves and is characterized by waveguide propagation characteristics.

[0006] The object of the invention is to provide an efficient and accurate distance measurement using radar in a pipe.

[0007] This object is achieved by the features specified in claims 1 and 16.

[0008] A method according to embodiments of the invention is used to determine a distance to a surface of a medium or to another radar target in a pipe using a radar measuring device. The method operates according to the principle of FMCW radar and comprises transmitting a radar transmission signal frequency-modulated according to the FMCW principle within the pipe, receiving a radar reception signal reflected back to the radar measuring device from the surface of the medium or from the other radar target in the pipe, mixing the radar reception signal with the radar transmission signal or a signal derived therefrom and generating an intermediate frequency signal, determining a frequency spectrum of the intermediate frequency signal or a signal derived therefrom using a fast Fourier transform, and detecting the position of the frequency peaks in the frequency spectrum. The method also comprises determining a dispersion correction to eliminate orReducing dispersion effects, applying the dispersion correction to the intermediate frequency signal or a signal derived therefrom and generating a dispersion-corrected signal and redetermining the position of the frequency peaks in the frequency spectrum of the dispersion-corrected signal by introducing a number of frequency support points in the range of the previously detected frequency peaks, determining the respective frequency amplitude selectively at the newly introduced frequency support points by means of discrete Fourier transform or by means of the Goertzel algorithm, determining the position of the frequency peaks in the frequency spectrum of the dispersion-corrected signal using the frequency amplitudes at the newly introduced frequency support points and deriving the distance to the surface of the medium or to the other radar target in the pipe from the position of the frequency peaks in the frequency spectrum.

[0009] In this method, the computationally intensive Fourier transformation of the intermediate frequency signal (or a signal derived from it) and the subsequent peak detection are performed only once in advance. This allows the rough location of the frequency peaks in the frequency spectrum to be known. Dispersion correction, which reduces or eliminates the dispersion effects occurring in the tube, is then applied to the intermediate frequency signal (or a signal derived from it), resulting in a dispersion-corrected signal.

[0010] To determine the exact position of the frequency peaks in the frequency spectrum of the dispersion-corrected signal, a number of frequency sampling points are introduced in the range of the frequency peaks. The frequency amplitudes at these frequency sampling points are determined using discrete Fourier transformation or the Goertzel algorithm. In this way, the position of the respective peak maximum of the frequency peaks in the frequency spectrum can be determined with high accuracy without the need for another computationally intensive Fourier transformation and repeated peak detection. It is sufficient to selectively determine the frequency amplitudes at some frequency sampling points using DFT or the Goertzel algorithm. From the exact position of the respective peak maximum, the distance to the surface of the medium or to the other radar target in the pipe can then be derived with high accuracy.

[0011] Due to the significantly reduced computational effort, the spectral analysis of the dispersion-corrected signal can be performed in a much shorter time than before, resulting in a precise distance measurement within a very short time. This method enables distance measurements with submillimeter accuracy.

[0012] Advantageous further developments of the invention are specified in the subclaims.

[0013] The invention is explained in more detail below with reference to several embodiments shown in the drawing.

[0014] They show: Fig. 1A a tank with a stilling well and a radar measuring device for carrying out a level measurement in the stilling well; Fig. 1B a tank with a bypass pipe arranged outside the tank and with a radar measuring device for carrying out a level measurement in the bypass pipe; Fig. 2A is a block diagram of a distance sensor based on the FMCW principle; Fig. 2B shows the temporal course of the frequency of a transmitted and received signal; Fig. 3 the dependence of the propagation velocity on the frequency for a particular mode in a pipe; Fig. 4 the effect of a dispersion correction, which leaves the position of the frequency peaks in the frequency spectrum largely unchanged; Fig. 5 a flow chart for performing a dispersion correction in which the Fourier transformation and peak detection are carried out once in advance before the iteration loop; Fig. 6 a frequency peak in a frequency spectrum whose peak maximum is to be determined; Fig. 7 a simplified flow chart for performing a dispersion correction; Fig. 8A a possibility to determine the peak maximum by continued interval halving; Fig. 8B shows Brent’s method for approximating a peak in the vicinity of a peak maximum using parabolas; and Fig. 9 a schematic representation of a phase evaluation. Principle of level measurement in a pipe using radar

[0015] In Fig. 1A shows a tank 100 partially filled with a medium 101. A vertical surge pipe 102 is arranged in the tank 100 and extends into the medium 101. The medium 101 can be, for example, a liquid, but can also be a free-flowing bulk material. The surge pipe 102 is open at its lower end. Furthermore, the wall of the surge pipe 102 has a number of openings 103 so that the fill level of the medium 101 inside the surge pipe 102 corresponds to the fill level of the medium 101 outside the surge pipe 102. The surge pipe 102 is provided, on the one hand, to calm movements of the medium 101 in the tank 100. The surge pipe 102 thus serves as a "wave breaker." In addition, the surge well 102 can be used to determine the fill level of the medium 101.

[0016] Previously, mechanical methods were used for this purpose, whereas today, level measurement is carried out within the stilling well 102 using radar. For this purpose, a radar measuring device 104 is mounted at the upper end of the stilling well 102. The radar measuring device 104 comprises a radar transmitter unit that generates a radar transmission signal and couples it into the stilling well 102 via the waveguide transition 105. The transmitted radar signal is reflected within the stilling well 102 at the surface of the medium 101 and sent back to the radar measuring device 104. The radar measuring device 104 comprises a radar receiver unit that receives and evaluates the reflected radar signal. The fill level of the medium 101 can then be determined based on the radar reception signal.

[0017] The use of the stilling pipe 102 offers a number of advantages for level measurement in tank 100. For example, the wall of the stilling pipe 102 ensures that even when the surface of the medium 101 within the stilling pipe 102 is highly agitated, the surface remains relatively still. Even if foam forms inside the tank, the foam can hardly influence the measurement in the stilling pipe 102. If a level measurement is to be carried out inside a relatively small container, there is often not enough space inside the container for a radar measuring device. However, there is sufficient space for a stilling pipe with a comparatively small diameter. The radar measuring device can then be placed outside the container. A further advantage is that the radar waves are concentrated by the stilling pipe 102 onto a comparatively small area. This results in a stronger reflection signal.This is particularly advantageous when the medium 101 is a liquid with a low dielectric constant, which has comparatively poor reflection properties. Using a stilling well produces a reflected signal of sufficient intensity even for such liquids. The use of a stilling well also offers advantages when the medium is a toxic or hazardous chemical. The stilling well 102 enables the installation of an additional ball valve, which tightly seals the tank 100 when the radar measuring device 104 needs to be removed. In this case, the tank 100 does not need to be emptied before removing the radar measuring device 104.

[0018] To determine the fill level, a radar measurement according to the FMCW (Frequency Modulated Continuous Wave) principle is preferably carried out.

[0019] Fig. 1B shows a further embodiment in which the fill level in a tank 106 is determined by means of a bypass pipe 107 arranged outside the tank 106. The tank 106 is partially filled with a medium 108, for example with a liquid or with a free-flowing bulk material. The bypass pipe 107 is a vertical pipe arranged outside the tank 106, which is connected to the tank 106 via a lower connecting pipe 109 and an upper connecting pipe 110. Therefore, the bypass pipe 107 is partially filled with the medium 108, wherein the fill level of the medium 108 within the bypass pipe 107 corresponds to the fill level of the medium 108 in the tank 106. A fill level measurement is carried out within the bypass pipe 107 using radar. For this purpose, a radar measuring device 111 is attached to the upper end of the bypass pipe 107. The radar measuring device 111 comprises a radar transmitter unit that generates a radar transmission signal and couples it into the bypass tube 107.The radar transmission signal reaches the surface of the medium 108 within the bypass pipe 107 and is reflected back from the surface of the medium 108 to the radar measuring device 111. The radar measuring device 111 comprises a radar reception unit that receives and evaluates the radar signal reflected from the surface of the medium 108. Based on the radar reception signal, the fill level of the medium 108 in the bypass pipe 107 and thus also the fill level of the medium 108 in the tank 106 can be determined.

[0020] To determine the fill level, a radar measurement according to the FMCW (Frequency Modulated Continuous Wave) principle is preferably carried out. Distance measurement using radar according to the FMCW principle

[0021] In radar distance measurement based on the FMCW (Frequency-Modulated Continuous Wave) principle, a frequency-modulated radar signal is transmitted in continuous wave mode and reflected from the target. The reflected signal is received and evaluated by the distance sensor.

[0022] Fig. Figure 2A shows a block diagram of a distance sensor operating according to the FMCW principle. The transmission branch of the distance sensor includes a signal generator 200, which generates a frequency-modulated signal. The signal generated by the signal generator 200 is fed to an amplifier 202 via a frequency multiplication stage 201, in which the signal frequency is multiplied according to a predetermined factor. There, the signal is amplified and then fed to a transmission port 203. The frequency-modulated radar transmission signal is output via the transmission port 203.

[0023] In Fig. Figure 2B shows the frequency of the generated transmission signal 213 as a function of time. It can be seen that the frequency of the transmission signal 213 alternately increases and decreases linearly, resulting in an overall triangular curve. During a first modulation period T0, the frequency of the transmission signal is increased linearly from frequency f0 to frequency f0 + Δf0, where the value Δf0 is referred to as the frequency deviation. During a subsequent second modulation period T0, the frequency is linearly reduced back to f0, starting from f0 + Δf0. As an alternative to the triangular curve, the frequency of the transmission signal could also have a sawtooth-shaped frequency curve.

[0024] The frequency f s (t) of the transmitted signal 213 increases as a function of time with the slope S: fs(t)=f0+S⋅t

[0025] The slope S is determined by the frequency deviation Δf0 and the modulation period T0: S=Δf0T0

[0026] The frequencies of radar transmission signals, for example, range from approximately 4 GHz to 100 GHz. The frequency deviation Δf0 could be several GHz, for example. The modulation period could be selected from the range between approximately 0.1 ms and 5 ms, for example. These figures serve only to illustrate typical orders of magnitude; however, solutions outside these ranges are also possible.

[0027] As in Fig. As shown in Figure 2A, a portion of the emitted transmission signal is reflected back to the distance sensor by a target 204 located at a distance R from the distance sensor. The radar signal requires a propagation time τ for the path from the transmitting gate 203 to the target 204 and back to the receiving gate 205.

[0028] The reflected signal is received by the receiving port 205 of the distance sensor and fed to a receiving mixer 206. In the receiving mixer 206, the received signal is mixed with the currently transmitted signal. The resulting mixer signal 207 is filtered by a sampling low-pass filter 208, which suppresses frequency components above a cutoff frequency. The sampling low-pass filter 208 limits the bandwidth of the mixer signal 207 before digitization. Furthermore, the cutoff frequency determines a maximum distance R. maxThe low-pass filtered intermediate frequency signal 209 is sampled and digitized by an analog-to-digital converter 210. The resulting digitized intermediate frequency signal 211 contains target frequency components for one or more targets, from which the corresponding target distances can be determined. The digitized intermediate frequency signal 211 is fed to the digital signal processing unit 212 for evaluation, which determines the frequency components contained in the intermediate frequency signal. The distances can then be determined directly from the frequency peaks of the frequency spectrum.

[0029] Distance sensors in Fig. 2A can be used, for example, as level measuring devices in process measurement technology to determine the distance to a surface of a liquid or bulk material in a container. Signal propagation in free field

[0030] If the transmitted signal 213 is radiated freely (so-called "free-field case"), the signal propagates at the speed of light c. Part of the radiated transmitted signal is reflected back to the distance sensor by the target 204.

[0031] For this free-field case, the propagation time τ required by the signal for the route from the transmitting unit to the target 204 and back to the receiving unit can be expressed as follows: τ=2⋅Rc

[0032] Where R is the target distance and c is the speed of light in air. The speed of light in air c is related to the speed of light c0 in vacuum by the relationship c=c0εr together, where ε r the dielectric constant of air.

[0033] During the propagation time τ required by the radar signal, the transmission signal 213 generated by the signal generator continues to increase, so that the frequency of the currently emitted transmission signal is higher than the frequency of the reception signal. The reception signal 214, which is time-shifted by the propagation time τ, for the free-field case is shown in Fig. 2B shown in dashed lines.

[0034] As a result of the propagation time τ of the radar signal, there is a frequency difference between the transmitted and received signal that is characteristic of the propagation time τ and is known as the target frequency f Ziel For the free-field case, the target frequency f Ziel from the slope S of the transmitted signal and the propagation time τ. For the free-field case, the target frequency f Ziel to fTarget=S⋅τ=S⋅2⋅Rc

[0035] Since the quantities S and c are constant, in the free field case there is a direct proportionality between the target frequency f Zieland the corresponding target distance R. From the target frequency f Ziel The target distance R can therefore be directly derived. Signal propagation in a pipe

[0036] The propagation of a radar signal in a tube differs significantly from that of a radar signal in a free field because the tube's walls limit and guide the wave propagation. For the radar signal, the tube acts as a circular waveguide.

[0037] Taking into account the conditions for circular waveguides, the differential equation for wave propagation in circular waveguides can be derived from Maxwell's equations. The solution to this differential equation is the Bessel function, which describes the propagation behavior of the radar signal in the circular waveguide.

[0038] This results in different modes for signal propagation in the circular waveguide. Modes are specific electric and magnetic field configurations that can propagate within the waveguide. There are basically two different types of modes in the waveguide: The TE m,n -modes (transverse electrical) and the TM m,n -modes (transverse magnetic). In the TE m,n -modes, the electric field vector is oriented perpendicular to the propagation direction of the wave. In the TM m,n -Modes the magnetic field vector is oriented perpendicular to the propagation direction of the wave.

[0039] A characteristic of the propagation of electromagnetic waves in waveguides is that the electromagnetic wave can only propagate in the waveguide if its frequency is above a defined cutoff frequency f cFor electromagnetic waves with a frequency below this characteristic cutoff frequency f c no wave propagation is possible in the waveguide. The cutoff frequency f c is different for each fashion and can be calculated individually for each fashion.

[0040] For a TE mode TE m,n the corresponding cutoff frequency f c,mn as follows: fc,mn=c⋅χ'mnπ⋅D

[0041] In this equation, χ' mn the n-th zero of the derivative of the m-th Bessel function J m (x), c denotes the speed of light in air, and D denotes the diameter of the circular waveguide (i.e. the tube).

[0042] For a TM mode TM m,n the corresponding cutoff frequency f c,mn as follows: fc,mn=c⋅χmnπ⋅D

[0043] In this equation, χ mnthe n-th zero of the m-th Bessel function J m (x), c denotes the speed of light in air, and D denotes the diameter of the circular waveguide (i.e. the tube).

[0044] In the free-field case, radar waves propagate in air at the speed of light c. Therefore, in the free-field case, the propagation speed does not depend on the frequency of the radar signal.

[0045] In the waveguide, the individual modes propagate with a group velocity v g which is proportional to the speed of light c in air by a factor of β rel,mn related to: vg=c⋅βrel,mn

[0046] The factor β rel,mn looks like this: βrel,mn=1−(fc,mnf)2

[0047] Where f denotes c,mn is the cutoff frequency of the respective mode and f is the frequency of the radar signal. The factor β rel,mn returns values ​​in the range between 0 and 1.

[0048] Overall, the group velocity v g a mode in the waveguide can be expressed as follows: vg=c⋅1−(fc,mnf)2

[0049] The antenna structure for coupling the radar signal into the pipe is preferably designed so that the energy is used essentially only to excite a single mode. Since each mode has a different propagation behavior, the formation of many different modes is to be avoided during radar measurements in pipes. False or blurred echoes resulting from the different propagation times of the various superimposed modes would otherwise be the result. Excitation of the TE mode is particularly advantageous. 01, because the field configuration of this mode is particularly well suited for propagation in the pipe.

[0050] In the following, we will discuss the case where essentially only one mode is excited to a significant extent.

[0051] To illustrate the propagation behavior of radar signals in the waveguide, Fig. 3 the group velocity v g in the waveguide as a function of frequency. On the right axis of Fig. 3 is the cutoff frequency f c,mn for a specific mode. For frequencies below this cutoff frequency, no wave propagation in the waveguide is possible. Wave propagation in the waveguide begins at the cutoff frequency f c,mn . With increasing frequency, the group velocity v g in the waveguide and increasingly approaches the speed of light c in air.

[0052] Based on Fig. 3 it can be seen that the group velocity v gThe propagation speed of the radar signal in the waveguide, i.e., the propagation speed of the radar signal in the waveguide, is strongly dependent on the frequency of the radar signal. Radar signal components of different frequencies propagate at different speeds in the waveguide.

[0053] When measuring the level in a pipe, a frequency-modulated radar signal is injected into the pipe according to the principles of FMCW radar. Since the frequency of the injected FMCW radar signal is determined according to the Fig. As the ramp shown in Figure 2B varies, the propagation speed of the radar signal also varies. The different propagation speeds cause smearing and scattering of the reflected radar signal, which must be evaluated by the radar measuring device. This frequency dependence of the propagation speed is referred to as dispersion. The effects caused by this frequency-dependent propagation speed, in particular the smearing and scattering of the reflected signal, are referred to as dispersive effects. A correction for these dispersive effects will be derived below. Dispersion-induced effects on the phase response of the intermediate frequency signal

[0054] The transmission signal of an FMCW radar in the form of a frequency ramp can be determined according to equation (1) by its instantaneous frequency f s (t) can be described as: fs(t)=f0+S⋅t

[0055] Here, f0 denotes the starting frequency and S the slope of the frequency ramp. Starting at the starting frequency f0, the frequency increases linearly with a slope S. The slope S is determined by the frequency deviation Δf0 and the modulation period T0 according to equation (2): S=Δf0T0

[0056] In general, the transmitted signal can be described by its instantaneous phase φ s (t) specify: s(t)=cos(φs(t))

[0057] The instantaneous phase φ s (t) can be calculated by integration from the instantaneous frequency f s (t) can be calculated: φs(t)=2π∫0tfs(t¯)dt¯=2πf0t+πSt2+φs,0

[0058] The transmitted signal travels within the pipe to a radar target. The radar target could be, for example, the surface of the liquid or bulk solid. The transmitted signal is reflected from this radar target at a distance R and travels back to the radar measuring device. This results in a frequency-dependent delay time τ(f), which, due to the linearly increasing ramp, can also be easily written as a function of time t: τ(t)=2⋅Rc⋅βrel(f) =2⋅Rc⋅1−(fc,mnfs(t))2 =2⋅Rc⋅1−(fc,mnf0+S⋅t)2

[0059] The following applies to the received signal: e(t)=cos(φe(t)) φe(t)=2π∫0tfs(t¯−τ(t¯))dt¯=2π∫0tf0+S⋅(t¯−τ(t¯))dt¯=2 π∫0tf0+S⋅t¯−Sτ(t¯)dt¯=2πf0t+πSt2−2πS⋅∫0tτ(t¯)dt¯+φe,0

[0060] To generate the intermediate frequency signal, the Fig. 2A, the transmit signal is mixed with the receive signal to generate the intermediate frequency signal. The filtered intermediate frequency signal reflects (assuming an ideal mixer) the phase difference between the phase φ s (t) of the transmitted signal and the phase φ e (t) of the received signal. Mixing the transmitted signal and the received signal results in an intermediate frequency signal that can be represented as follows: z(t)=cos(φz(t)) φz(t)=φs(t)−φe(t)=2πS⋅∫0tτ(t¯)dt¯+Δφ=2π2SRc⋅∫0t1βrel(f0+S⋅t¯)dt¯+Δφ=2π2Rc(f0+fc+St)(f0−fc+St)(f0 +St)f02+2f0St+S2t2−fc2(f0+St)2|t=0t+Δφ=2π2Rc⋅(f0+St)2−fc2|t=0t+Δφ=2π2Rc⋅((f0+St)2−fc2−f02−fc2)+Δφ

[0061] This equation summarizes the dispersive effects in the phase response of the intermediate frequency signal caused by the frequency dependence of the group velocity. All time-independent phase contributions are summarized in the initial phase Δφ. Determination of the starting phase Δφ

[0062] All time-independent phase contributions of the phase φ z (t) of the intermediate frequency signal were combined in the starting phase Δφ. This starting phase Δφ will be determined below. The starting phase Δφ can be calculated from the difference between the phase φ s (t) of the transmitted signal and the phase φ e (t) of the received signal at time t=0.

[0063] The phase φ s (t) of the transmitted signal can be written according to equation (11) as: φs(t)=2π∫0tfs(t¯)dt¯=2πf0t+πSt2+φs,0

[0064] Regarding the phase φ e(t) of the received signal, an estimate is made to determine the starting phase Δφ. To determine the starting phase Δφ, it is assumed that the propagation time τ is constant and independent of the frequency. Therefore, as in the free-field case, dispersion is neglected to determine the starting phase Δφ. Strictly speaking, this approach is incorrect for a pipe, because in a pipe, the propagation velocity and thus also the propagation time τ depend on the frequency of the radar signal. Nevertheless, the following expression, which assumes a constant, frequency-independent propagation time τ, can be used to estimate the starting phase Δφ of the intermediate frequency: φe(t)=φs(t−τ)=2πf0(t−τ)+πS⋅(t−τ)2+φs,0=2πf0t−2πf0τ+πSt2+πSτ2−2πStτ+φs,0

[0065] For the starting phase Δφ we then get: Δφ=φs(0)−φe(0)==2πf0τ(0)+πSτ2(0)

[0066] According to equation (12), τ(0) is: τ(0)=2⋅Rc⋅βrel(f0)

[0067] This results in the starting phase φ z (0) to: φz(0)=Δφ=2πf02Rc⋅βrel(f0)+πS(2Rc⋅βrel(f0))2mod 2π Derivation of a dispersion correction

[0068] The intermediate frequency signal z(t) can be interpreted as the radar system's range response after a Fourier transformation. Due to the nonlinear phase response, the Fourier transformation results in a blurring of the target response in the spectral domain.

[0069] In the following, the possibilities for evaluating the intermediate frequency signal under the influence of dispersion and taking into account other sources of error will be discussed.

[0070] According to embodiments of the invention, a correction for the dispersion influence on the phase is performed prior to further analysis. Such a dispersion correction counteracts broadening and blurring of the peaks in the spectral range.

[0071] In the following, an additive phase correction is derived, which is applied to the phase of the intermediate frequency signal before further evaluation. This dispersion correction has the task, on the one hand, of reducing or eliminating the phase variation caused by dispersion according to equation (16). In addition, a phase that increases linearly with time is added, as it would be in a system with a constant, frequency-independent group velocity v const The diameter D of the waveguide or the resulting cutoff frequency f cinto the calculation. The cutoff frequency derived from the measured diameter D and subject to measurement uncertainty is referred to below as f c This results in the following phase correction: φz,corr(t)=2π2Rc⋅((f0+St)2−f^c2−f02−f^c2)−2π2RSvconst⋅t

[0072] The first term 2π2Rc⋅((f0+St)2−f^c2−f02−f^c2) serves to reduce or eliminate the phase progression caused by dispersion.

[0073] The second term −2π2RSvconst⋅t is used to add a phase that increases linearly with time and occurs at a constant, frequency-independent group velocity v const The constant frequency-independent propagation velocity v const can be freely defined within certain limits. For example, v const be defined as group velocity at frequency f0: v const = c·ß rel(f0), or v const can be defined as the speed of light c in air: v const = C ,

[0074] It is particularly advantageous to use the constant frequency-independent propagation velocity v const as group velocity at the center frequency f mitte the in Fig. 2B. The constant propagation velocity v const is therefore defined as the propagation speed at the frequency f mitte vconst=c⋅βrel(fmitte) where the center frequency f mitte the frequency ramp can be represented as: fmitte=f0+S⋅T02. Dependence of the dispersion correction on the target distance R

[0075] From equation (21) it can be seen that both the first term and the second term of the phase correction φ z,corr(t) depends on the target distance R, which is not yet known at the time the phase correction is determined. The target distance R is yet to be determined.

[0076] To obtain the phase correction φ described by equation (21) z,corr To be able to carry out (t) anyway, there are various options: A first possibility is to estimate the target distance R by evaluating the non-dispersion-corrected intermediate frequency signal supplied by the receive mixer 206. Although the target distance thus obtained is not exact, it can be used for a first determination of the phase correction φ z,corr (t) can be used.

[0077] A second option for estimating the target distance is possible if the fill level of a container is determined cyclically at regular intervals. In this case, it can be assumed that the fill level changes slowly and continuously. Therefore, two consecutively determined fill level measurements are relatively close to each other. In this respect, a previous fill level measurement can serve as an estimate for the current fill level measurement. Based on this assumption, a previous fill level measurement can be used as an estimate for the target distance. Iterative determination of the target distance R and the phase correction (φ z,corr (t) in mutual dependence

[0078] Even higher accuracy can be achieved by using an iterative procedure. Here, an estimate of the target distance serves as the starting point for determining the dispersion correction (P z,corr(t). The dispersion correction φ z,corr (t) is used to correct the intermediate frequency signal, and based on the dispersion-corrected intermediate frequency signal, an improved, more accurate value of the target distance R can be determined. Using this more accurate value of R, the dispersion correction is determined again and used to correct the intermediate frequency signal. The dispersion-corrected intermediate frequency signal thus obtained can then be used to determine the target distance R with even greater accuracy, etc. In this respect, the target distance R and the dispersion correction φ z,corr (t) are determined iteratively in mutual dependence. Over the course of several iterations, the target distance R converges to its actual value and also the dispersion correction φ z,corr(t) becomes increasingly accurate, so that dispersive effects are increasingly eliminated. This iterative approach yields very accurate values ​​for the target distance R and the dispersion correction φ after just a few iterations. z,corr (t). Evaluation of the phase-corrected intermediate frequency signal

[0079] If the dispersion correction term φ is subtracted z,corr (t) from the measured phase, ideally (with an error-free known pipe diameter) a phase curve remains that increases linearly with time, which is caused by the second term of equation (21): φc(t)=φz(t)−φz,corr(t)=2π2RSvconst⋅t

[0080] From this we obtain the target frequency component f Ziel: fTarget=ω2π=12πddtφc(t)=2RSvconst

[0081] The target distance R can then be derived from the target frequency component determined in this way: R=fTarget⋅vconst2S

[0082] For evaluation, exactly the propagation speed v const which was already used in equation (21) to generate the linearly increasing second phase term. So if there v const = c·β rel (f mitte ) was set, then v will be used again for evaluation. const = c·β rel (f mitte ) used. No change in the starting phase φ z (0) by the phase correction

[0083] From equation (21) it can be seen that for t = 0 the starting phase φ z (0) is not changed by the phase correction. This starting phase can therefore also be read from the result of the complex Fourier transform at the position of the magnitude maximum in the spectral domain (modulo 2π). For the phase φ z (0) therefore still applies according to equation (20): φz(0)=2πf02Rc⋅βrel(f0)+πS(2Rc⋅βrel)2mod 2π

[0084] Applying dispersion correction does not affect the phase information of the intermediate-frequency signal. Even after applying dispersion correction to the phase, the phase information can still be used for further signal analysis. Therefore, after performing phase correction, both the magnitude and phase of the intermediate-frequency signal can be used for further analysis. It should be noted that the phase is significantly less sensitive to small disturbances, whereas a pure analysis of the magnitude spectrum already reveals significant deviations in the exact determination of the maximum position. Advantageous choice of propagation velocity at the center frequency of the frequency ramp

[0085] In the dispersion correction of equation (21), the second term serves to add a phase that increases linearly with time and that increases at a constant, frequency-independent group velocity v const The constant frequency-independent propagation velocity v const can be freely determined within certain limits. It has already been discussed that it is particularly advantageous to use the constant frequency-independent propagation velocity v const as group velocity at the center frequency f mitte the in Fig. 2B. The constant propagation velocity v const is therefore defined as the propagation speed at the frequency f mitte vconst=c⋅βrel(fmitte) where the center frequency f mitte the frequency ramp can be represented as: fmitte=f0+S⋅T02

[0086] The dispersion correction according to equation (21) is applied to the time signal, where the constant propagation velocity v const the propagation velocity at the center frequency f mitte the frequency ramp is selected. This selection of v const = c· β rel (f mitte ) has the particular advantage that the position of the frequency peaks in the frequency spectrum is only slightly affected by the dispersion correction. The frequency peak corresponding to the radar target remains almost at the same position after the dispersion correction as before the dispersion correction. By using the constant propagation velocity v const = c·β rel (f mitte ) the position of the frequency spectrum with respect to the frequency axis therefore shifts only insignificantly, which significantly simplifies further evaluation.

[0087] In Fig. Figure 4 shows schematically how the original frequency spectrum is changed by applying the dispersion correction when the constant propagation velocity v const the propagation velocity at the center frequency f mitte the frequency ramp is used. In Fig. Figure 4 shows a comparison of the original frequency spectrum 400 before dispersion correction and the corrected frequency spectrum 401 after application of dispersion correction. The frequency is plotted along the right axis, and the frequency amplitude is plotted along the vertical axis. In the original frequency spectrum 400, the peaks 402 and 403 are broadened and smeared due to dispersion. By applying dispersion correction, the broadened original peaks 402 and 403 are transformed into the corrected peaks 404 and 405. The corrected peaks 404 and 405 are significantly better defined and also significantly narrower than the original peaks 402 and 403 broadened by dispersion. Fig. 4 it can be seen that the corrected peaks 404, 405 are located at the same positions in the frequency spectrum as the original peaks 402, 403. This is a consequence of the fact that in the dispersion correction of equation (21) the propagation velocity v const the propagation velocity at the center frequency f mitte the frequency ramp. This choice of v const This means that the position of the frequency peaks in the frequency spectrum is only slightly changed by the dispersion correction. This also has the advantage that the iterative implementation of the dispersion correction requires fewer iterations than previously to determine the final target frequency and the associated target distance. Dispersion correction process

[0088] In the Fig. The flowchart shown in Figure 5 shows how the Fig. 2A can be evaluated by iteratively applying a dispersion correction to determine the target frequency components and the target distances with high accuracy. Fig. The evaluation scheme shown in Figure 5 takes advantage of the fact that a dispersion correction with v const = c·β rel (f mitte ) only slightly influences the position of the peaks in the frequency spectrum. Therefore, the position of the peaks in the frequency spectrum can be determined by a preliminary fast Fourier transformation followed by peak detection.

[0089] The starting point is the Fig. 2A. The digitized intermediate frequency signal 211 is a real-valued time signal. In the optional step 500, a so-called "column averaging" is first performed. If not just one but several frequency ramps are executed during a measurement, the corresponding values ​​of several sample series can be averaged. This occurs during the collumn averaging in step 500. The collumn averaging serves to improve the signal-to-noise ratio of the digital time signal.

[0090] In the subsequent step 501, the DC component of the time signal is removed. This step is therefore also referred to as "DC removal." For this purpose, the mean value of the time samples is first determined, and this mean value is then subtracted from each of the time samples. The result is corrected time samples that no longer contain any DC component.

[0091] In the subsequent step 502, the DC-corrected discrete-time intermediate frequency signal is "windowed." This means that the values ​​of the discrete-time real signal are weighted with a window function to avoid undesirable effects caused by the limitation of the observation window.

[0092] In the next step 503, a Hilbert transform of the real-valued time signal is performed. Using the Hilbert transform, the real and imaginary parts of a complex-valued signal can be mapped to each other. In this case, the Hilbert transform is used in step 503 to generate an associated imaginary part for the real-valued intermediate frequency signal, thus providing a complete complex-valued time signal. This complete complex-valued time signal then serves as the output signal for performing the iterative dispersion correction in the subsequent iterative dispersion correction loop 504.

[0093] In parallel with the Hilbert transformation performed in step 503, a fast Fourier transform (FFT) of the real-valued time signal is performed in step 505. The result of the Fourier transformation is a real-valued, discrete-time frequency spectrum that includes a corresponding frequency peak for each target frequency component contained in the intermediate frequency signal.

[0094] In the subsequent step 506, peak detection of the peaks in the frequency spectrum is performed. To detect the peaks in the frequency spectrum, for example, it can be determined at which points in the frequency spectrum the frequency sample values ​​lie above a predetermined threshold. By comparing the frequency sample values ​​with a threshold, the position of the frequency peaks in the frequency spectrum can be determined, at least roughly.

[0095] After the peak positions in the frequency spectrum have been roughly determined in step 506, a fine determination of the peak positions is performed in the subsequent step 507. For this purpose, a number of frequency support points are introduced in the region of a peak position detected in step 506, and the corresponding frequency amplitude is then determined for each of these frequency support points.

[0096] The principle of this selective refinement of the frequency sampling in the vicinity of the peak maxima is described in Fig. 6 illustrates. Fig. Figure 6 shows a section of the frequency spectrum 600 obtained as a result of the fast Fourier transform performed in step 505. The frequency is plotted along the right axis, and the frequency amplitude is plotted along the vertical axis. Based on the frequency samples 601 provided by the FFT in step 505, the peak 602 was detected in step 506.

[0097] To finely determine the maximum of peak 602, a number of frequency support points 603 are introduced in step 507 in the region of the initially only roughly known peak maximum. The corresponding frequency amplitude is determined for each of the frequency support points 603. To selectively determine the spectral amplitude at the frequency support points 603, either the discrete Fourier transform (DFT) can be calculated or the Goertzel algorithm can be applied.

[0098] The Goertzel algorithm enables efficient calculation of the frequency amplitudes of individual spectral components. Therefore, the use of the Goertzel algorithm is particularly advantageous when not the entire frequency spectrum is to be determined, but only a few spectral components at selected frequencies. Using the Goertzel algorithm, it is particularly possible to determine individual frequency amplitudes at specific frequencies with comparatively little computational effort. A description of the Goertzel algorithm can be found, for example, in the textbook "Digital Signal Processing, Principles, Algorithms and Applications," 3 rd Edition, John G. Proakis, Dimitris G. Manolakis, Prentice-Hall, Chapter 6, pages 480-481. This brief description of the Goertzel algorithm is hereby incorporated by reference into the description of the present patent application.

[0099] Using frequency support points 603 and the associated frequency amplitudes, the profile of spectrum 600 in the region of the maximum of peak 602 can be determined with high accuracy. For example, several frequency support points can first be introduced in the region of a frequency peak, and the frequency amplitude is determined at each of these frequency support points. In the regions where the determined frequency amplitudes are highest, additional frequency support points can then be selectively introduced to further refine the frequency resolution, and the frequency amplitude is determined at each of these frequency support points. In this way, the exact position 604 of the peak maximum can be determined with high accuracy. This provides the target frequency associated with a specific radar target.

[0100] As a result of the fine determination of the peak positions in step 507, the target frequency is obtained, from which a first, not yet dispersion-corrected value R1 of the target distance can be obtained: R1=fTarget⋅vconst2S where the propagation velocity v const the propagation velocity at the center frequency f mitte is used. The target distance R1 thus determined is fed to the dispersion correction loop 504.

[0101] Based on the Fig. From the flowchart shown in Figure 5, it can be seen that the fast Fourier transformation in step 505 and the peak detection in step 506 are performed only once in advance. This is possible because the position of the peaks will no longer change significantly due to the dispersion correction performed within the dispersion correction loop 504. If v const is elected as v const = c·β rel (f mitte), then the dispersion correction does not lead to a significant change in the position of the peaks. Therefore, it is sufficient to perform the fast Fourier transformation 505 and peak detection 506 only once in advance, which significantly accelerates the evaluation process.

[0102] The target distance R1 determined in step 507 is fed to the dispersion correction loop 504 and serves as a starting point for determining the dispersion correction during the first iteration of the dispersion correction loop 504. According to equation (21), the first phase correction φ z,corr,1 (t) can be written as φz,corr,1(t)=2π2R1c⋅((f0+St)2−f^c2−f02−f^c2)−2π2R1⋅Svconst⋅t where v const = c·β rel (f mitte ) is the propagation velocity at the center frequency of the frequency ramp.

[0103] The dispersion correction φ calculated in step 508 z,corr,1(t) is applied to the now complex-valued discrete-time intermediate frequency signal in the mixer stage 509. The phase correction performed in the mixer stage 509 can be written as φc(t)=φz(t)−φz,corr,1(t)

[0104] Here, φ z (t) the phase of the intermediate frequency signal before correction, φ z,corr,1 (t) denotes the phase correction determined in step 508, and φ c (t) denotes the corrected phase of the intermediate frequency signal.

[0105] As an alternative to the previously described representation, in which a phase correction term is added (or subtracted) to the phase of the intermediate frequency signal, the phase correction can also be expressed by forming a quotient. In this case, the complex-valued measured intermediate frequency signal is divided by a complex-valued correction signal to obtain a phase-corrected intermediate frequency signal. Fig. The mixer stage 509 shown in Figure 5 is designed to perform this complex-valued quotient formation and to generate a dispersion-corrected complex-valued signal whose phase has been corrected according to the dispersion effects calculated in step 508.

[0106] For this dispersion-corrected intermediate frequency signal, a fine determination of the peak positions is performed again in the subsequent step 510 in order to determine the target frequency components and the target distance based on the dispersion-corrected signal. It is not necessary to perform a further Fourier transformation and a further peak detection within the dispersion correction loop 504. Since the propagation velocity v is used for determining the dispersion correction, const the propagation velocity at the center frequency f mittethe frequency ramp was used, it can be assumed that the position of the frequency peaks in the frequency spectrum does not change significantly due to the application of the dispersion correction in the mixer stage 509. Therefore, within the dispersion correction loop 504, a repeated execution of the Fourier transformation and the subsequent peak detection can be omitted. It can be assumed that the approximate peak positions determined in step 506 are still correct. Therefore, within the dispersion correction loop 504, a fine determination of the peak positions can be carried out directly in step 510. This fine determination of the peak positions in the frequency spectrum is again carried out according to the Fig. 6 is performed. A number of frequency support points 603 are introduced in the vicinity of the peak position already approximately known from step 506, and for each of these frequency support points 603, the corresponding frequency amplitude is recalculated based on the dispersion-corrected time signal. To calculate the frequency amplitude at the frequency support points 603, a discrete Fourier transform (DFT) can be performed, for example, or the Goertzel algorithm can be used.

[0107] Since complex-valued signal processing is performed within the phase correction loop 504, it is advantageous to use the "generalized Goertzel algorithm" to determine the frequency amplitudes at the frequency support points 603. This algorithm, based on a complex-valued time signal, delivers a complex-valued frequency amplitude for a specific frequency support point. The complex-valued time signal is thus converted into complex-valued frequency amplitudes. The generalized Goertzel algorithm therefore delivers, in addition to the magnitude of the frequency amplitude, associated phase information. This phase information for the individual frequency amplitudes can be used in a phase evaluation to precisely determine the frequency of the peak maximum, as described below.A description of the generalized Goertzel algorithm can be found in the article “Goertzel-Algorithm Generalized to Non-Integer Multiples of Fundamental Frequency”, Sysel and Rajmic, EURASIP Journal on Advances in Signal Processing, 2012, 2012: 56, which is hereby incorporated by reference into the description of the present patent application.

[0108] Based on the frequency amplitudes determined for the individual frequency support points 603, the precise position 604 of the peak maximum of the dispersion-corrected peak 602 can then be determined. The frequency of the peak maximum is the target frequency for a specific target. The target frequency thus determined can then be converted into a target distance R2 using equation (28).

[0109] In the subsequent step 511, it is determined whether the value R2 of the target distance is already sufficiently accurate or whether further iterations of the dispersion correction loop 504 must be performed to obtain an even more accurate value for the target distance. For example, in step 511, it can be queried whether the difference between the currently determined target distance and the target distance determined one iteration previously is greater than a specified epsilon. As long as the difference is still greater than the specified epsilon, the iteration continues. As soon as the value falls below the specified epsilon, the value of the target distance no longer changes significantly with further iterations, and the iteration can be aborted.

[0110] The iterations within the dispersion correction loop 504 are performed until both the target distance R and the phase correction φ z,corr(t) are determined with sufficient accuracy. In the first pass, in step 508, the first phase correction φ z,corr,1 (t) and applied to the intermediate frequency signal. By evaluating the phase-corrected intermediate frequency signal, the more precise target distance R2 was then determined. Based on R2, an even more precise phase correction φ could now be calculated in a further iteration in step 508. z,corr,2 (t) and applied to the intermediate frequency signal. Using the thus phase-corrected intermediate frequency signal, a third, even more precise target distance value R3 could then be determined, and so on.

[0111] These iterations continue until it is determined in step 511 that the determined target range no longer changes significantly. In this case, both the target range and the phase correction have converged to their final values.

[0112] In the subsequent optional step 512, a phase evaluation can also be performed to determine the distance with even greater accuracy. This phase evaluation takes advantage of the fact that the generalized Goertzel algorithm also provides a phase in addition to the frequency amplitude at the respective frequency support points. Therefore, the corresponding phase is also known for the frequency amplitude at the peak maximum of a frequency peak. By comparing this phase at the peak maximum with a previously determined or calculated target phase profile, this phase information can be converted into distance information.

[0113] As a result of the Fig. 5, a precisely determined distance 513 to the surface of the medium or to another radar target in the pipe is obtained.

[0114] In the Fig. In the process shown in Figure 5, the computationally intensive Fourier transformation and the subsequent peak detection are performed only once in advance in steps 505 and 506. This significantly reduces both the computational effort and the time required for distance determination, and the distance value is available with high accuracy after a short time. In particular, in the Fig. 5, it is not necessary to perform a fast Fourier transformation within the dispersion correction loop 504. Since the peaks in the frequency spectrum shift only slightly, it is sufficient to perform a selective determination of the frequency amplitudes at selected frequency support points using DFT or the Goertzel algorithm. The time required for such a calculation is significantly less than the time required to perform a full Fourier transformation.

[0115] Another advantage of the Fig. 5 is that only a small number of iterations are required within the dispersion correction loop 504 until the final dispersion correction or the final value of the distance is determined. This small number of iterations is mainly due to the fact that a dispersion correction that is required for the propagation velocity v const = c·β rel (f mitte ) is carried out, the position of the frequency peaks in the frequency spectrum remains largely unchanged. Due to the small number of iterations, the computational effort and thus also the time required for determining the distance is significantly reduced, so that a precise distance value can be provided after only a small number of iterations. In particular, with the help of the Fig. 5, a measurement accuracy in the sub-millimeter range can be achieved when measuring the level in the stilling pipe. Simplified evaluation scheme

[0116] In many cases, a single iteration is sufficient to determine the distance with a sufficiently high accuracy. If only a single iteration of the dispersion correction loop 504 is performed, the result shown in Fig. 7. The starting point is again the intermediate frequency signal 211. In optional step 700, a set averaging is first performed, whereby the measured values ​​obtained for several frequency ramps are averaged. Subsequently, in step 701, the DC component of the measured values ​​is removed, and in step 702, a window function is applied to the measured values. Using the Hilbert transformation performed in step 703, the real-valued signal is supplemented to form a complex-valued signal. In addition, in step 704, a fast Fourier transform of the intermediate frequency signal is performed, and the result is the frequency spectrum of the intermediate frequency signal. In the following step 705, the frequency peaks in the frequency spectrum are detected. In step 706, a fine determination of the frequency peaks in the frequency spectrum is performed.For this purpose, several frequency support points are first introduced in the region of the peak maximum, and the respective associated frequency amplitude is then determined for each of these frequency support points using discrete Fourier transformation or the Goertzel algorithm. From the peak maximum, an initial value for the distance to the respective radar target is obtained using equation (29), which is then used in the subsequent step 707 to calculate a dispersion correction. In mixer 708, the now complex-valued intermediate frequency signal is corrected according to the dispersion correction determined in step 707, and a dispersion-corrected signal is obtained. In step 709, a fine determination of the frequency peaks in the frequency spectrum of the now dispersion-corrected signal is again carried out.For this purpose, the respective frequency amplitudes at several frequency support points in the range of the frequency peaks are determined, and based on these frequency amplitudes, the respective peak maximum of a frequency peak can then be determined. From this, the distance to the respective radar targets can then be derived. In optional step 710, a phase evaluation can be performed to determine the distance with even greater accuracy by taking the phase information into account. The result of the calculation in . Fig. The flow diagram shown in Figure 7 gives the distance 711 to the radar target(s) in the tube.

[0117] Refinement of the frequency spectrum by introducing frequency support points There are various options for introducing frequency support points, three of which are described in more detail below.

[0118] According to a first approach, several frequency support points are first introduced, and the respective frequency amplitude is determined at these frequency support points using DFT or the Goertzel algorithm. Subsequently, to improve the frequency resolution, an additional frequency support point is introduced in the region of a frequency peak, midway between two adjacent frequency support points. By continuously halving the intervals, the resolution of the frequency spectrum can be refined as desired.

[0119] According to a second possibility, the frequency intervals between adjacent frequency support points are subdivided asymmetrically by introducing additional frequency support points, with the golden ratio being a possible division ratio. By continuing to subdivide intervals according to the golden ratio, any desired resolution of the frequency spectrum can also be achieved.

[0120] A third option is to use Brent's method to determine the peak frequency. This method is described, for example, in Chapter 10.2 of the standard work Numerical Recipes in C: the Art of Scientific Computing, William H. Press, 2nd ed. 1992. First, at least three frequency support points are introduced in the region of a frequency peak, and the respective frequency amplitude is determined at these frequency support points using DFT or the Goertzel algorithm. A first approximate parabola is then placed through these points, which approximates the spectrum curve in the vicinity of the peak maximum. The vertex of this approximate parabola is introduced as a further frequency support point, which is used to determine a second approximate parabola. The second approximate parabola approximates the spectrum curve in the vicinity of the peak maximum with even greater accuracy.In this way, the peak frequency can be obtained as the vertex of a series of converging approximate parabolas.

[0121] Based on Fig. 8A illustrates the method of continued interval halving. In Fig. Figure 8A shows a peak 800 of the frequency spectrum. The frequency is plotted along the right-hand axis, and the frequency amplitude is plotted along the vertical axis. First, three frequency support points 801, 802, 803 are introduced at the frequencies f1, f2, and f3, and the frequency amplitude for each of these frequency support points is determined using DFT or the Goertzel algorithm. This relatively coarse frequency grid is now to be further subdivided by introducing additional frequency support points. For this purpose, the frequency interval 804 between the frequencies f1 and f2 is subdivided in the middle to define another frequency support point f4. The frequency amplitude corresponding to the frequency f4 is determined using DFT or the Goertzel algorithm. This yields point 805 of the frequency spectrum.Likewise, the frequency interval 806 between the frequency f2 and the frequency f3 is divided in the middle to define the additional frequency support point f5. The frequency amplitude corresponding to the frequency f5 is determined using DFT or the Goertzel algorithm. This yields point 807 of the frequency spectrum. From the five points 801, 805, 802, 807, 803 found so far, the three neighboring points with the highest frequency amplitudes are now selected. In the example of . Fig. 8A, these are the three points 805, 802, and 807. To further refine the frequency spectrum, the frequency interval 808 between the frequencies f4 and f2 is divided in half to define another frequency support point f6. The frequency amplitude at frequency f6 is determined using DFT or the Goertzel algorithm, resulting in point 809. Similarly, the frequency interval 810 between the frequencies f2 and f5 is divided in half, and the result of this interval halving is the next frequency support point f7. The frequency amplitude at frequency f7 is determined using DFT or the Goertzel algorithm, resulting in point 811. As soon as a desired resolution of the frequency spectrum is achieved, the interval halving is aborted. The frequency of the point for which the highest frequency amplitude was determined so far is then output as the peak frequency.

[0122] According to the second method for continued interval division, the frequency intervals between neighboring points in the vicinity of a peak are each subdivided asymmetrically according to a predetermined division ratio. For example, the frequency intervals can be subdivided according to the golden ratio. This asymmetric subdivision defines additional frequency support points, and the frequency amplitudes at these frequency support points are determined using DFT or the Goertzel algorithm. The neighboring points with the highest frequency amplitudes serve as the basis for the next iteration. In some cases, the asymmetric subdivision of the frequency intervals can positively influence the convergence behavior.

[0123] In Fig. Figure 8B illustrates how the maximum of a peak in the frequency spectrum can be determined using Brent's method. Brent's method is described, for example, in Chapter 10.2 of the standard work "Numerical Recipes in C: the Art of Scientific Computing," William H. Press, 2nd ed. 1992, and is hereby incorporated by reference into the disclosure of this application.

[0124] In Fig. Figure 8B shows a peak 850 of the frequency spectrum. The frequency is plotted along the right axis, and the frequency amplitude is plotted along the vertical axis. First, three frequency support points 851, 852, and 853 are determined at frequencies f8, f9, and f 10introduced, and the frequency amplitude for each of these frequency support points is determined using DFT or the Goertzel algorithm. In the first step of Brent's method, the peak 850 is approximated by a first approximation parabola 854, which is determined by the frequency support points 851, 852, 853 and the associated frequency amplitudes. The first approximation parabola 854 has its vertex 855 at the frequency f 11 . This frequency f 11 of the vertex 855 is used as an additional frequency support point for the next iteration of the parabolic approximation. For this purpose, the frequency amplitude at the additional frequency support point f 11calculated using DFT or the Goertzel algorithm. This yields point 856 of the frequency spectrum. For the next iteration, the three frequency support points 852, 856, and 853 of the spectrum, which exhibit the highest frequency amplitudes determined so far, are used. Using these three frequency support points 852, 856, and 853 and the associated frequency amplitudes, a second approximate parabola 857 is defined, which approximates the course of peak 850 in the vicinity of the peak maximum even better than the first approximate parabola 854. The second approximate parabola 857 has its apex 858 at the frequency f 12 . The frequency f 12 could already be considered a sufficiently accurate approximation for the peak maximum. If the accuracy is considered sufficient, the calculation would be aborted at this point. Alternatively, the accuracy could possibly be further improved by adjusting the frequency f12 of the vertex 858 is used as an additional frequency support point for a further iteration of the parabolic approximation.

[0125] The advantage of Brent's method is that the course of a peak in the vicinity of its maximum already resembles a parabola, and the course of the peak in the vicinity of the peak maximum can be very well approximated by an approximate parabola. Therefore, if the peak course is approximated by a series of approximate parabolas, these approximate parabolas converge very quickly. Carrying out a phase evaluation

[0126] It has already been discussed that to determine the peak maximum of the frequency peaks in the frequency spectrum, several frequency support points are introduced, and the corresponding frequency amplitudes are then determined for these frequency support points. The generalized Goertzel algorithm can be used to determine the frequency amplitudes. In addition to the frequency amplitude, the generalized Goertzel algorithm also provides a phase. This additional phase information can be used to further improve the accuracy of distance determination through phase evaluation.

[0127] Based on Fig. Figure 9 describes how such a phase analysis is performed. The target distance is plotted in meters along the right axis, and the phase of the frequency component in question in the frequency spectrum is plotted in radians along the vertical axis. Fig.Figure 9 shows the target curve 900 of the phase of the frequency component under consideration in the intermediate frequency signal as a function of the target distance. It can be seen that the target curve 900 has a sawtooth shape.

[0128] By determining the peak maximum of the frequency peak under consideration in the frequency spectrum, a target distance 901 and an associated phase 902 are known. As illustrated by arrow 903, the point 904 corresponding to phase 902 on the target curve of phase 900 is now sought. The question is therefore which point 904 on the target curve 900 of the phase would provide the determined phase 902. The target distance 905 corresponding to this point 904 is considered a better and more credible value of the target distance than the original value 901 of the target distance. In other words, the phase of the peak maximum is trusted more than the frequency of the peak maximum. The phase evaluation therefore provides an improved value 905 for the target distance.

Claims

[1] Method for determining a distance to a surface of a medium (101, 108) or to another radar target in a pipe (102, 107) by means of a radar measuring device (104, 111) which operates according to the principle of FMCW radar, the method comprising: a) transmitting a radar transmission signal (213) frequency-modulated according to the FMCW principle within the tube (102, 107), b) receiving a radar reception signal reflected back to the radar measuring device (104, 111) at the surface of the medium (101, 108) or at the other radar target in the pipe (102, 107), c) mixing the radar reception signal with the radar transmission signal (213) or a signal derived therefrom and generating an intermediate frequency signal (211), d) determining (505) a frequency spectrum of the intermediate frequency signal or a signal derived therefrom by means of a fast Fourier transform and detecting (506) the position of the frequency peaks in the frequency spectrum, e) determining (508) a dispersion correction to eliminate or reduce dispersion effects, applying the dispersion correction to the intermediate frequency signal or a signal derived therefrom and generating a dispersion-corrected signal, f) Redetermining (510) the position of the frequency peaks in the frequency spectrum of the dispersion-corrected signal by f1) introducing a number of frequency support points (603) in the range of the frequency peaks detected in step d), f2) determining the respective frequency amplitude selectively at the newly introduced frequency support points (603) by means of discrete Fourier transformation or by means of the Goertzel algorithm, f3) Determining the position (604) of the frequency peaks in the frequency spectrum of the dispersion-corrected signal using the frequency amplitudes at the newly introduced frequency support points (603) and deriving the distance (513) to the surface of the medium or to the other radar target in the pipe from the position (604) of the frequency peaks in the frequency spectrum. [2] Method according to claim 1, characterized by that dispersion correction is a phase correction which, on the one hand, reduces or eliminates a dispersion-dependent phase component in the phase response of the intermediate frequency signal and, on the other hand, adds a phase component which is not dependent on dispersion effects to the phase response of the intermediate frequency signal. [3] Method according to claim 1 or claim 2, characterized by that the dispersion correction depends on the distance to the surface of the medium or to the other radar target in the pipe. [4] Method according to one of claims 1 to 3, characterized by that to determine the dispersion correction, a propagation velocity of the radar transmission signal in the pipe at a center frequency of the frequency ramp of the radar transmission signal is used. [5] Method according to claim 4, characterized by at least one of the following: - the center frequency is determined by fmitte=f0+S⋅T02, where f0 is the starting frequency of the frequency ramp, S is the slope of the frequency ramp and T0 is the modulation period of the radar transmission signal; - when determining the dispersion correction, the choice of the propagation velocity at the center frequency of the frequency ramp results in the dispersion correction changing the positions of the frequency peaks in the frequency spectrum only insignificantly. [6] Method according to one of claims 1 to 5, characterized by at least one of the following: - the dispersion correction comprises a dispersion-dependent term designed to reduce or eliminate the dispersion-dependent phase component in the phase response of the intermediate frequency signal; - the dispersion correction comprises a dispersion-dependent term designed to reduce or eliminate the dispersion-dependent phase component in the phase response of the intermediate frequency signal, the dispersion-dependent term of the dispersion correction having the following form: 2π2Rc⋅((f0+St)2−f^c2−f02−f^c2), where R is the distance to the surface of the medium or to the other radar target in the tube, where c is the speed of light in air, where f0 is the starting frequency of the frequency ramp and S is the slope of the frequency ramp of the radar transmission signal, and where f̂ c the cutoff frequency of a dominant mode in the tube; - the phase fraction not dependent on dispersion effects, which is added by the dispersion correction, increases linearly with time; - the non-dispersion-dependent phase component added by the dispersion correction depends on the distance to the surface of the medium or to the other radar target in the pipe; - the dispersion correction comprises a non-dispersion-dependent term designed to add the phase component not dependent on dispersion effects to the phase response of the intermediate frequency signal, wherein the phase component not dependent on dispersion effects increases linearly with time; - the dispersion correction comprises a non-dispersion-dependent term designed to add the phase component not dependent on dispersion effects to the phase response of the intermediate frequency signal, the phase component not dependent on dispersion effects depending on the distance to the surface of the medium or to the other radar target in the pipe; - the dispersion correction comprises a non-dispersion-dependent term designed to add the phase component not dependent on dispersion effects to the phase response of the intermediate frequency signal, the non-dispersion-dependent term of the dispersion correction having the following form: −2π2RSvconst⋅t, where R is the distance to the surface of the medium or to the v const other radar target in the tube, where S is the slope of the frequency ramp of the radar transmission signal, and where v consta propagation speed of the radar transmission signal, which can be freely determined. [7] Method according to one of claims 1 to 6, characterized by that step d) is carried out only once in advance. [8] Method according to one of claims 1 to 7, characterized by that steps e) and f) are repeated in mutual dependence until the distance to the surface of the medium or to the other radar target in the pipe is determined with a predetermined accuracy. [9] Method according to one of claims 1 to 8, characterized by following steps: a) Introducing some frequency support points in the area of ​​the detected frequency peaks, b) Determining the corresponding frequency amplitudes at these frequency support points using discrete Fourier transformation or the Goertzel algorithm, c) Introduction of additional frequency support points to further refine the frequency resolution in the frequency ranges where the frequency amplitudes are highest, d) Determining the corresponding frequency amplitudes at the further frequency support points using discrete Fourier transformation or the Goertzel algorithm. [10] Method according to claim 9, characterized by that steps c) and d) are repeated several times to determine the position of the peak maximum. [11] Method according to one of claims 1 to 10, characterized by that the position of the peak maximum of the frequency peak is determined based on the frequency amplitudes at at least three frequency support points in the range of a frequency peak by means of parabolic interpolation according to the Brent method. [12] Method according to one of claims 1 to 11, characterized bythat the frequency amplitudes at the newly introduced frequency support points are determined using the generalized Goertzel algorithm, whereby the generalized Goertzel algorithm provides a phase in addition to the magnitude of the frequency amplitude. [13] Method according to claim 12, characterized by that the phase provided by the generalized Goertzel algorithm for each newly introduced frequency support point is used to determine the phase at the peak maximum of a frequency peak [14] Method according to claim 12 or claim 13, characterized by that a desired phase curve of the frequency amplitude is determined or calculated as a function of the distance to the surface of the medium or to the other radar target in the pipe, and wherein with the aid of this desired phase curve the phase at the peak maximum of a frequency peak is converted into a more precise value of the distance to the surface of the medium or to the other radar target in the pipe. [15] Method according to one of claims 1 to 14, characterized by at least one of the following: - the medium is a liquid or a bulk material; - the pipe is a stilling pipe or a bypass pipe; - the method is used to determine the level of the medium in the pipe from the distance to the surface of the medium; - the method is used in a radar measuring device to determine the distance to radar targets using FMCW radar; - the method is used in a level measuring device to determine a level using FMCW radar; - the method is used in the context of a level measurement using FMCW radar to determine the level in a container or tank. [16] Radar measuring device (104, 111) for determining a distance to a surface of a medium (101, 108) or to another radar target in a pipe (102, 107), the radar measuring device operating according to the FMCW principle and comprising: a radar transmitting / receiving unit designed to generate a radar transmitting signal (213) that is frequency-modulated according to the FMCW principle, to receive a radar receiving signal reflected back from the surface of the medium (101, 108) or from the other radar target in the pipe (102, 107), to convert the radar receiving signal into an intermediate frequency signal (211) by mixing it with the radar transmitting signal (213) or a signal derived therefrom, and to determine a distance to the surface of the medium (101, 108) or to the other radar target in the pipe (102, 107) on the basis of the intermediate frequency signal (211) thus obtained, characterized by that the radar measuring device (104, 111) is designed to • to determine a frequency spectrum of the intermediate frequency signal or a signal derived therefrom by means of a fast Fourier transformation (505) and to detect the position of the frequency peaks in the frequency spectrum (506), • to determine a dispersion correction to eliminate or reduce dispersion effects (508), to apply the dispersion correction to the intermediate frequency signal or a signal derived therefrom and to generate a dispersion-corrected signal, • to redetermine (510) the position of the frequency peaks in the frequency spectrum of the dispersion-corrected signal by introducing a number of frequency support points (603) in the area of ​​the detected frequency peaks, by determining the respective frequency amplitude selectively at the newly introduced frequency support points (603) by means of discrete Fourier transformation or by means of the Goertzel algorithm, by determining the position (604) of the frequency peaks in the frequency spectrum of the dispersion-corrected signal using the frequency amplitudes at the newly introduced frequency support points (603) and by deriving the distance (513) to the surface of the medium or to the other radar target in the pipe from the position (604) of the frequency peaks in the frequency spectrum. [17] Radar measuring device according to claim 16, characterized by at least one of the following: - the medium is a liquid or a bulk material; - the pipe is a stilling pipe or a bypass pipe; - the radar measuring device is designed to determine the level of the medium in the pipe from the distance to the surface of the medium; - the radar measuring device is designed as a field device which can be connected to a controller via a fieldbus; - The radar measuring device is a level measuring device for process automation.

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